Cartesian closed topological categories and tensor products
In the last years, the concept of Cartesian closed category has proved its utility not only for Mathematics but also for Computer Science. It is useful to study its properties in order to obtain more applications. In this context, this paper deals with the relationships between the tensor closedness of \({\mathcal M}od_{R}({\mathcal X})\), the category of \(R\)-module objects in a category \({\mathcal X}\) (where \(R\) is itself a ring object of \({\mathcal X}\)) and the Cartesian closedness of \({\mathcal X}\). It is shown, for example, that if \({\mathcal X}\) is Cartesian closed topological, then \({\mathcal M}od_{R}({\mathcal X})\) is tensor closed, and, moreover, is a monoidal category w.r.t. the same tensor product.
scientific article; zbMATH DE number 2176362